Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and angle α.

Triangle has two solutions: a=3.3; b=5.4; c=2.34395772776 and a=3.3; b=5.4; c=7.80991030269.

#1 Obtuse scalene triangle.

Sides: a = 3.3   b = 5.4   c = 2.34395772776

Area: T = 2.16604929007
Perimeter: p = 11.04395772776
Semiperimeter: s = 5.52197886388

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 145.9677067521° = 145°58'1″ = 2.54876059277 rad
Angle ∠ C = γ = 14.03329324787° = 14°1'59″ = 0.24549208755 rad

Height: ha = 1.30993896368
Height: hb = 0.88001825558
Height: hc = 1.8476908774

Median: ma = 3.82202501121
Median: mb = 0.94443574106
Median: mc = 4.31993280196

Inradius: r = 0.39114086285
Circumradius: R = 4.82442772603

Vertex coordinates: A[2.34395772776; 0] B[0; 0] C[-2.73547628747; 1.8476908774]
Centroid: CG[-0.13217285324; 0.6165636258]
Coordinates of the circumscribed circle: U[1.17697886388; 4.68803040098]
Coordinates of the inscribed circle: I[0.12197886388; 0.39114086285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 34.03329324787° = 34°1'59″ = 2.54876059277 rad
∠ C' = γ' = 165.9677067521° = 165°58'1″ = 0.24549208755 rad




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 3.3 ; ; b = 5.4 ; ; c = 2.34 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 3.3+5.4+2.34 = 11.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.04 }{ 2 } = 5.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.52 * (5.52-3.3)(5.52-5.4)(5.52-2.34) } ; ; T = sqrt{ 4.67 } = 2.16 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.16 }{ 3.3 } = 1.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.16 }{ 5.4 } = 0.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.16 }{ 2.34 } = 1.85 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 3.3**2-5.4**2-2.34**2 }{ 2 * 5.4 * 2.34 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.4**2-3.3**2-2.34**2 }{ 2 * 3.3 * 2.34 } ) = 145° 58'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.34**2-3.3**2-5.4**2 }{ 2 * 5.4 * 3.3 } ) = 14° 1'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.16 }{ 5.52 } = 0.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.3 }{ 2 * sin 20° } = 4.82 ; ;





#2 Obtuse scalene triangle.

Sides: a = 3.3   b = 5.4   c = 7.80991030269

Area: T = 7.21113504486
Perimeter: p = 16.50991030269
Semiperimeter: s = 8.25545515135

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 34.03329324787° = 34°1'59″ = 0.59439867259 rad
Angle ∠ C = γ = 125.9677067521° = 125°58'1″ = 2.19985400773 rad

Height: ha = 4.37105154234
Height: hb = 2.67108705365
Height: hc = 1.8476908774

Median: ma = 6.50875759729
Median: mb = 5.35222000189
Median: mc = 2.18662016098

Inradius: r = 0.87436211091
Circumradius: R = 4.82442772603

Vertex coordinates: A[7.80991030269; 0] B[0; 0] C[2.73547628747; 1.8476908774]
Centroid: CG[3.51546219672; 0.6165636258]
Coordinates of the circumscribed circle: U[3.90545515135; -2.83333952359]
Coordinates of the inscribed circle: I[2.85545515135; 0.87436211091]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 145.9677067521° = 145°58'1″ = 0.59439867259 rad
∠ C' = γ' = 54.03329324787° = 54°1'59″ = 2.19985400773 rad

Calculate another triangle

How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 3.3 ; ; b = 5.4 ; ; c = 7.81 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 3.3+5.4+7.81 = 16.51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.51 }{ 2 } = 8.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.25 * (8.25-3.3)(8.25-5.4)(8.25-7.81) } ; ; T = sqrt{ 52 } = 7.21 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.21 }{ 3.3 } = 4.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.21 }{ 5.4 } = 2.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.21 }{ 7.81 } = 1.85 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 3.3**2-5.4**2-7.81**2 }{ 2 * 5.4 * 7.81 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.4**2-3.3**2-7.81**2 }{ 2 * 3.3 * 7.81 } ) = 34° 1'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.81**2-3.3**2-5.4**2 }{ 2 * 5.4 * 3.3 } ) = 125° 58'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.21 }{ 8.25 } = 0.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.3 }{ 2 * sin 20° } = 4.82 ; ; : Nr. 1




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